TitoloGlobal survival of branching random walks and tree-like branching random walks
Autore/iBertacchi D.; Coletti C.F.; Zucca F.
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AbstractThe local critical parameter $\lambda_s$ of continuous-time branching random walks is completely understood and can be computed as a function of the reproduction rates. On the other hand, only for some classes of branching random walks it is known that the global critical parameter $\lambda_w$ is a certain function of the reproduction rates, which we denote by $ 1/K_w$. We provide here new sufficient conditions which guarantee that the global critical parameter equals $ 1/K_w$. This result extends previously known results for branching random walks on multigraphs and general branching random walks. We show that these sufficient conditions are satisfied by periodic tree-like branching random walks. We also discuss the critical parameter and the critical behaviour of continuous-time branching processes in varying environment. So far, only examples where $\lambda_w=1/K_w$ were known; here we provide an example where $\lambda_w>1/K_w$.